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Simplifying x2 + -15x + -198 = 0 Reorder the terms: -198 + -15x + x2 = 0 Solving -198 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + -15x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + -15x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + -15x + x2 = 0 + 198 -15x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 -15x + x2 = 198 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 198 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 198 + 56.25 Combine like terms: 198 + 56.25 = 254.25 56.25 + -15x + x2 = 254.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 254.25 Calculate the square root of the right side: 15.945218719 Break this problem into two subproblems by setting (x + -7.5) equal to 15.945218719 and -15.945218719.Subproblem 1
x + -7.5 = 15.945218719 Simplifying x + -7.5 = 15.945218719 Reorder the terms: -7.5 + x = 15.945218719 Solving -7.5 + x = 15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 15.945218719 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 15.945218719 + 7.5 x = 15.945218719 + 7.5 Combine like terms: 15.945218719 + 7.5 = 23.445218719 x = 23.445218719 Simplifying x = 23.445218719Subproblem 2
x + -7.5 = -15.945218719 Simplifying x + -7.5 = -15.945218719 Reorder the terms: -7.5 + x = -15.945218719 Solving -7.5 + x = -15.945218719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -15.945218719 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -15.945218719 + 7.5 x = -15.945218719 + 7.5 Combine like terms: -15.945218719 + 7.5 = -8.445218719 x = -8.445218719 Simplifying x = -8.445218719Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.445218719, -8.445218719}
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